The Resource A Stability Technique for Evolution Partial Differential Equations : A Dynamical Systems Approach, by Victor A. Galaktionov, Juan Luis Vázquez, (electronic resource)

A Stability Technique for Evolution Partial Differential Equations : A Dynamical Systems Approach, by Victor A. Galaktionov, Juan Luis Vázquez, (electronic resource)

Label
A Stability Technique for Evolution Partial Differential Equations : A Dynamical Systems Approach
Title
A Stability Technique for Evolution Partial Differential Equations
Title remainder
A Dynamical Systems Approach
Statement of responsibility
by Victor A. Galaktionov, Juan Luis Vázquez
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
common feature is that these evolution problems can be formulated as asymptoti­ cally small perturbations of certain dynamical systems with better-known behaviour. Now, it usually happens that the perturbation is small in a very weak sense, hence the difficulty (or impossibility) of applying more classical techniques. Though the method originated with the analysis of critical behaviour for evolu­ tion PDEs, in its abstract formulation it deals with a nonautonomous abstract differ­ ential equation (NDE) (1) Ut = A(u) + C(u, t), t > 0, where u has values in a Banach space, like an LP space, A is an autonomous (time-independent) operator and C is an asymptotically small perturbation, so that C(u(t), t) ~ ° as t ~ 00 along orbits {u(t)} of the evolution in a sense to be made precise, which in practice can be quite weak. We work in a situation in which the autonomous (limit) differential equation (ADE) Ut = A(u) (2) has a well-known asymptotic behaviour, and we want to prove that for large times the orbits of the original evolution problem converge to a certain class of limits of the autonomous equation. More precisely, we want to prove that the orbits of (NDE) are attracted by a certain limit set [2* of (ADE), which may consist of equilibria of the autonomous equation, or it can be a more complicated object
Member of
http://library.link/vocab/creatorName
Galaktionov, Victor A
Dewey number
515.353
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • 8oSqLadZ_SQ
  • n1LiqZEdZWA
Image bit depth
0
Language note
English
LC call number
QA370-380
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Vázquez, Juan Luis.
Series statement
Progress in Nonlinear Differential Equations and Their Applications,
Series volume
56
http://library.link/vocab/subjectName
  • Differential equations, partial
  • Global analysis (Mathematics)
  • Mechanics
  • Mechanics, Applied
  • Hydraulic engineering
  • Partial Differential Equations
  • Analysis
  • Solid Mechanics
  • Engineering Fluid Dynamics
Label
A Stability Technique for Evolution Partial Differential Equations : A Dynamical Systems Approach, by Victor A. Galaktionov, Juan Luis Vázquez, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Introduction: A Stability Approach and Nonlinear Models -- Stability Theorem: A Dynamical Systems Approach -- Nonlinear Heat Equations: Basic Models and Mathematical Techniques -- Equation of Superslow Diffusion -- Quasilinear Heat Equations with Absorption. The Critical Exponent -- Porous Medium Equation with Critical Strong Absorption -- The Fast Diffusion Equation with Critical Exponent -- The Porous Medium Equation in an Exterior Domain -- Blow-up Free-Boundary Patterns for the Navier-Stokes Equations -- The Equation ut = uxx + uln2u: Regional Blow-up -- Blow-up in Quasilinear Heat Equations Described by Hamilton-Jacobi Equations -- A Fully Nonlinear Equation from Detonation Theory -- Further Applications to Second- and Higher-Order Equations -- References -- Index
Dimensions
unknown
Edition
1st ed. 2004.
Extent
1 online resource (XIX, 377 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461220503
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-2050-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089817
  • (SSID)ssj0001298525
  • (PQKBManifestationID)11766360
  • (PQKBTitleCode)TC0001298525
  • (PQKBWorkID)11242219
  • (PQKB)11197277
  • (DE-He213)978-1-4612-2050-3
  • (MiAaPQ)EBC3076669
  • (EXLCZ)993400000000089817
Label
A Stability Technique for Evolution Partial Differential Equations : A Dynamical Systems Approach, by Victor A. Galaktionov, Juan Luis Vázquez, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Introduction: A Stability Approach and Nonlinear Models -- Stability Theorem: A Dynamical Systems Approach -- Nonlinear Heat Equations: Basic Models and Mathematical Techniques -- Equation of Superslow Diffusion -- Quasilinear Heat Equations with Absorption. The Critical Exponent -- Porous Medium Equation with Critical Strong Absorption -- The Fast Diffusion Equation with Critical Exponent -- The Porous Medium Equation in an Exterior Domain -- Blow-up Free-Boundary Patterns for the Navier-Stokes Equations -- The Equation ut = uxx + uln2u: Regional Blow-up -- Blow-up in Quasilinear Heat Equations Described by Hamilton-Jacobi Equations -- A Fully Nonlinear Equation from Detonation Theory -- Further Applications to Second- and Higher-Order Equations -- References -- Index
Dimensions
unknown
Edition
1st ed. 2004.
Extent
1 online resource (XIX, 377 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461220503
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-2050-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089817
  • (SSID)ssj0001298525
  • (PQKBManifestationID)11766360
  • (PQKBTitleCode)TC0001298525
  • (PQKBWorkID)11242219
  • (PQKB)11197277
  • (DE-He213)978-1-4612-2050-3
  • (MiAaPQ)EBC3076669
  • (EXLCZ)993400000000089817

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